ABSTRACT We present observations and analysis of rotation curves and dark matter halo density profiles in the central regions of four nearby dwarf galaxies. This observing program has been designed to overcome some of the limitations of other rotation curve studies that rely mostly on longslit spectra. We find that these objects exhibit the full range of central density profiles between constant density and NFW halos. This result suggests that there is a distribution of central density slopes rather than a unique halo density profile.

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We derive inner dark matter halo density profiles for a sample of 165 low-mass galaxies using rotation curves obtained from high-quality, long-slit optical spectra assuming minimal disks and spherical symmetry. For $\rho(r) \sim r^{-\alpha}$ near the galaxy center we measure median inner slopes ranging from $\alpha_m = 0.22 \pm 0.08$ to $0.28 \pm 0.06$ for various subsamples of the data. This is similar to values found by other authors, and in stark contrast to the intrinsic cusps ($\alpha_{int}\sim1$) predicted by simulations of halo assembly in cold dark matter (CDM) cosmologies. To elucidate the relationship between $\alpha_m$ and $\alpha_{int}$ in our data, we simulate long-slit observations of model galaxies with halo shapes broadly consistent with the CDM paradigm. Simulations with $\alpha_{int}=1/2$ and 1 recover both the observed distribution of $\alpha_m$ and correlations between $\alpha_m$ and primary observational parameters such as distance and disk inclination, whereas those with $\alpha_{int}=5/4$ are marginally consistent with the data. Conversely, the hypothesis that low-mass galaxies have $\alpha_{int}=3/2$ is rejected. While the simulations do not imply that the data favor intrinsic cusps over cores, they demonstrate that the discrepancy between $\alpha_m$ and $\alpha_{int}\sim1$ for our sample does not necessarily imply a genuine conflict between our results and CDM predictions: rather, the apparent cusp/core problem may be reconciled by considering the impact of observing and data processing techniques on rotation curves derived from long-slit spectra. Comment: 17 pages, 14 figures; uses emulateapj. Accepted for publication in AJ. Minor changes made to match AJ proofs

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We present a spectroscopic deprojection analysis of a sample of ten relaxed galaxy clusters. We use an empirical F-test derived from a set of Markov Chain Monte Carlo simulations to determine if the core plasma in each cluster could contain multiple phases. We derive non-parametric baryon density and temperature profiles, and use these to construct total gravitating mass profiles. We compare these profiles with the standard halo parameterizations. We find central density slopes roughly consistent with the predictions of LCDM: $-1 \lesssim d\log(\rho)/d\log(r) \lesssim -2$. We constrain the core size of each cluster and, using the results of cosmological simulations as a calibrator, place an upper limit of ~0.1 cm^2/g = 0.2 b(GeV/c^2)^{-1} (99% confidence) on the dark matter particle self-interaction cross section.

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The good agreement between large-scale observations and the predictions of the now-standard ΛCDM theory gives us hope that this will become a lasting foundation for cosmology. After briefly reviewing the current status of the key cosmological parameters, I summarize several of the main areas of possible disagreement between theory and observation: big bang nucleosynthesis, galaxy centers, dark matter substructure, and angular momentum, updating my earlier reviews [Primack, J.R., 2004. In: Ryder et al., S.D. (Eds.), IAU Symposium 220 Dark Matter in Galaxies (Astron. Soc. Pacific), p. 53 and p. 467, and other articles in that volume. Primack, J.R., 2003. Status of Cold Dark Matter Cosmology. In: Cline, D. (Ed.), Proceedings of 5th International UCLA Symposium on Sources and Detection of Dark Matter, February 2002. Nucl. Phys. B, Proc. Suppl., 124, 3 (astro-ph/0205391)]. The issues in all of these are sufficiently complicated that it is not yet clear how serious they are, but there is at least some reason to think that the problems will be resolved through a deeper understanding of the complicated astrophysics involved in such processes as gas cooling, star formation, and feedback from supernovae and AGN. Meanwhile, searches for dark matter are dramatically improving in sensitivity, and gamma rays from dark matter annihilation at the galactic center may have been detected by H.E.S.S.

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arXiv:astro-ph/0311259v1 11 Nov 2003**TITLE**ASP Conference Series, Vol. **VOLUME***, **YEAR OF PUBLICATION****NAMES OF EDITORS**Dark Matter in Dwarf Galaxies: High ResolutionObservationsAlberto D. Bolatto, Joshua D. Simon, Adam Leroy, & Leo BlitzRadio Astronomy Laboratory and Department of Astronomy, Universityof California at Berkeley, 601 Campbell Hall, Berkeley, CA 94720, USAAbstract.dark matter halo density profiles in the central regions of four nearbydwarf galaxies. This observing program has been designed to overcomesome of the limitations of other rotation curve studies that rely mostlyon longslit spectra. We find that these objects exhibit the full range ofcentral density profiles between ρ ∝ r0(constant density) and ρ ∝ r−1(NFW halo). This result suggests that there is a distribution of centraldensity slopes rather than a unique halo density profile.We present observations and analysis of rotation curves and1. IntroductionThe last few years have seen a flurry of activity in the field of precision measure-ments of central density profiles in dark matter halos, as demonstrated elsewherein these proceedings. Most of this activity has concentrated on addressing twoquestions: is there a unique central density profile slope?, and, more to thepoint, do the measurements agree with the predictions of the simulations? Infact, the observations appear to point to a substantial disagreement betweenthe central density profiles measured in low mass, low surface brightness dwarfgalaxies (e.g., de Blok et al. 2001) and the predictions of most Cold Dark Mat-ter simulations (e.g., Navarro, Frenk, & White 1996, hereafter NFW; Moore etal. 1999; Jing & Suto 2000). The significance of this discrepancy, however, isa matter of debate. Some authors ascribe it to intrinsic systematic problems inthe observations, which conspire to poorly constrain the central density slopes(e.g., Swaters et al. 2003a), while others acknowledge these problems but arguethat the data provide strong enough constraints to rule out universal slopes assteep as those predicted by the simulations (e.g., de Blok, Bosma, & McGaugh2003).Can observations be used to test the predictions of cosmological simula-tions? In the current era of “precision cosmology” the answer should be mostemphatically yes! Close attention needs to be paid to the potential systematiceffects, however, in order to minimize their importance. In this paper we presenta series of studies of high resolution velocity fields of dwarf galaxies which wehave designed to remove as much as possible the impact of systematic uncer-tainties. Our overall conclusion is that (as also suggested by de Blok et al. 2003)these objects appear to exhibit a range of central density profiles rather thana unique value. The discrepancy between observations and simulations is thusreal, and perhaps related to the absence of baryons and their related astrophysics1

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2Bolatto,Simon, Leroy, & Blitzin the simulations (although other explanations are also possible; e.g., Ricotti2003). In this regard, these observations should be taken as a reality check onfuture simulations that incorporate all the physics relevant on the small spatialscales.2. Experimental DesignSeveral systematic problems have been identified in the literature as potentialcauses of artificially shallow central density profiles. A problem that plaguedseveral earlier studies based on HI observations was the lack of angular resolu-tion and the consequent smearing of the possible central density cusp. To avoidthis pitfall, and to attain the best possible angular and spatial resolution, ourprogram targets nearby dwarf galaxies with a combination of high resolutionmillimeter interferometry (obtained at BIMA) and optical spectroscopy. Theuse of two wavelengths allows us to avoid the limitations inherent to one oranother tracer: because CO emission is faint and patchy, millimeter CO in-terferometry is signal–to–noise limited and can only be used on a few objects.However, it does provide 2D velocity fields and it is positionally extremely accu-rate. Conversely, Hα spectroscopy can be adversely affected by obscuration andpositioning problems. In particular, incorrect or inaccurate slit positioning inlongslit spectra can cause artificially flat rotation curves. To overcome this prob-lem we acquire integral field Hα spectroscopy of our targets using the DensePakmultifiber spectrograph at the WIYN telescope. To increase the positional accu-racy of the resulting Hα velocity field we cross–correlate the integrated intensityfrom the individual DensePak footprints with a narrow–band Hα image of thetarget. The 2D spectroscopic data allows us to study in detail the kinematicsof the galaxies, and in particular to look at the harmonic decomposition of thevelocity field in order to characterize their noncircular motions. Finally, we usemultiband optical and near–IR photometry to model and remove the contribu-tion of the stellar disk to the overall kinematics.Once the velocity fields are obtained, the data analysis proceeds as follows.The galaxy is deprojected and divided in concentric tilted rings, with center,position angle, and axis ratio determined using the available multiband pho-tometry. A function of the form vsys+ vcircosθ + vradsinθ (where θ is thedeprojected position angle measured from the major axis) is fitted to each ring,representing the effects of the systemic, circular, and radial velocities. Aftermaking sure that the kinematics traced by the radio and optical data agree,both datasets are combined to obtain an overall velocity field.A crucial part of any rotation curve study is to quantify the errors, whichhave direct bearing on the strenght of the constraints placed on the shape of thedensity profile. We use bootstrap simulations to estimate the final errors in thecenter position, position angle, and inclination of the galaxy; these errors thenare obtained from the data itself, and not derived from the fitted uncertainties ofthe individual velocity measurements which can be unrealistically small. Finally,a Monte Carlo simulation with the actual velocity field and these errors as inputparameters is used to determine the final uncertainties in the individual pointsof the rotation curve. The rotation curve thus produced is the starting point ofthe kinematic study.

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Dark Matter in Dwarf Galaxies: High Resolution Observations3 a)Vrotation (km s−1)0102030405060708090Galactocentric Radius (pc)100050015002000Vresidual (km s−1)Galactocentric Radius (")020 406080100120 140−20−100 b)Galactocentric Radius (pc)100050015002000Galactocentric Radius (")0 204060 80100120140Figure 1.tion curve measured before removing any contribution from the diskcomponent (“minimum disk” solution). The error bars incorporate theuncertainties in the geometrical parameters used for the inversion, asdescribed in the main text. The dashed and dotted lines show the cir-cular velocities due to the HI and H2components of the gaseous disk.The lower panel shows the residuals after removing a power law fit for14′′< r < 105′′, with the gray regions indicating 1σ and 2σ deviations(ρ ∝ r−0.27±0.09assuming a spherical halo). Panel (b) shows the resultof removing the contributions of the gaseous and the stellar disk (thickgray line) from the measured rotation. The stellar disk is maximal, witha mass–to–light ratio M∗/LK= 0.19M⊙/L⊙K. The fit to the densityprofile shows it is constant density inside 1.8 kpc (ρ ∝ r−0.01±0.12).Rotation curve of NGC 2976. Panel (a) shows the rota-The azimuthally averaged IR photometry of the galaxy is used to model thepotential of an infinitely thin stellar disk using Toomre’s method. The circularvelocity due to this disk is then subtracted in quadrature from the measuredrotation curve. The mass–to–light ratio of the stellar disk can in principle beobtained from the colors of the stellar population, either via population synthesismodels (such as the popular Starburst99), or using empirical relationships (e.g.,Bell & de Jong 2001). Similar procedures are followed to estimate the contribu-tions of the gaseous disk to the rotation, when data are available. The rotationcurve obtained after removing the disk contributions is used to obtain the darkmatter density profile. The density profiles quoted here assume spherical halos.3.ResultsWe have completed the type of study described above in five nearby dwarf galax-ies: NGC 2976 (Simon et al. 2003; Fig. 1), NGC 4605 (Bolatto et al. 2002; Fig.

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4Bolatto,Simon, Leroy, & Blitz a)Vrotation (km s−1)020406080100Galactocentric Radius (pc)100050015002000Vresidual (km s−1)Galactocentric Radius (")0 1020 3040 50 6070 80 90 100 110−20−100 b)Galactocentric Radius (pc)100050015002000Galactocentric Radius (")0 1020304050 607080 90100 110Figure 2.imum disk solution for this galaxy. The black line shows the powerlaw fit for r > 25′′(ρ ∝ r−1.1), which significantly overestimates therotation velocities for the innermost points. These are better fit withan almost constant density core (ρ ∝ r−0.4). Panel (b) shows the max-imum disk solution for this galaxy. After subtracting the contributionof a maximal exponential disk (thick gray curve), the density profile isfit by a ρ ∝ r−0.65±0.1power law at all radii. This study was carriedout using 2D CO velocity information and a 1D Hα longslit spectrum.We now have 2D Hα and HI data, and plan to revisit this object soon.Rotation curve of NGC 4605. Panel (a) shows the min-2), NGC 5949 (Fig. 3), NGC 5963 (Fig. 4), and NGC 4625. The latter galaxy ispart of an interacting pair with the associated problems in interpreting its veloc-ity field (in hindsight, a poor choice). In the other four cases, however, we havebeen able to measure central density profiles. Two of these galaxies (NGC 2976and NGC 4605) have measurable vradterms that are usually associated with thepresence of bars. Analysis of the multicolor images, surface photometry, andhigher order harmonic decomposition of the kinematics of NGC 2976, however,show no evidence for a bar. The radial motions in NGC 4605 are comparativelyless important, and it appears unlikely that it hosts a bar (because of its higherinclination, however, this case is less clear than that of NGC 2976). NeitherNGC 5949 nor NGC 5963 show measurable radial motions (vrad< 5 km s−1),although from the images the latter may contain a small bar.4.ConclusionsThe four galaxies in this series of studies for which we were able to retrievereliable central density profiles appear to span the full range of behaviors; fromconstant density cores to NFW halos. In particular, the data for NGC 2976

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Dark Matter in Dwarf Galaxies: High Resolution Observations5 a)Vrotation (km s−1)020406080100120140Galactocentric Radius (pc)10001500 500200025003000Vresidual (km s−1)Galactocentric Radius (")0 1020 30 4050−30−1501530 b)Galactocentric Radius (pc)10001500 500200025003000Galactocentric Radius (")0 1020 30 40 50Figure 3.imum disk solution and its power law fit (ρ ∝ r−0.87±0.1).(b) shows the result after removing the contribution from the disk(thick gray curve). In this case we have used a submaximal disk withM∗/LK= 0.5M⊙/L⊙K, similar to what is observed in the Milky Way(the maximal disk solution for NGC 5949 has M∗/LK≃ 0.8M⊙/L⊙K).This is a compromise solution: at the moment of writing these proceed-ings we lack enough photometry information to better constrain themass–to–light ratio of this galaxy. With the chosen M/L, the powerlaw fit to the dark matter halo density profile is ρ ∝ r−0.69±0.18.Rotation curve of NGC 5949. Panel (a) shows the min-Panelclearly do not allow an NFW halo. Because we have tried to eliminate mostof the systematics present in this type of measurement, we believe that thisrange of central density slopes is real and reflects an underlying distribution,although the caveats associated with a small sample certainly apply. To studythis distribution we plan to expand the sample of observed galaxies to 10–15objects in the near future. This larger sample will also allow us to look forcorrelations between central density slopes and other parameters, such as galaxymass or the magnitude of noncircular motions.Perhaps the most important conclusion, however, is that measurements ofthe central density profiles of dwarf galaxies can be accurate. Multiwavelengthimaging spectroscopy is key to minimize the vulnerability of these observationsto potential systematic problems, such as erroneous positioning of the spectro-graph slit. At the same time, 2D high–resolution data also provides a wealth ofkinematic information that would be otherwise unavailable.Finally, the presence of measurable radial motions in two out of the fourgalaxies studied presents a bit of a mystery; are we observing the remnants ofthe processes that erased the original central cusps? There does not appearto be a clear link to asymmetries or bars in our small sample, and maintainingsuch motions over long time periods appears very difficult in these small objects.